Question 1 A) Solve the equation below for x. 8x−5=358x−5=35(1 point) Responses x=154x=154x is equal to 15 fourths x=5x=5x is equal to 5 x=3x=3x is equal to 3 x=32x=32x is equal to 32 Question 2 A)What is the correct first step to solve the equation −3x−13=14−3x−13=14 for x?(1 point) Responses Subtract 13 from both sides of the equation. Subtract 13 from both sides of the equation. Add 13 to both sides of the equation. Add 13 to both sides of the equation. Divide both sides of the equation by -3. Divide both sides of the equation by -3. Add 3 to both sides of the equation. Add 3 to both sides of the equation. Question 3 A) Solve the equation below for k. k+56=4k+56=4(1 point) Responses k=19k=19k is equal to 19 k=15k=15k is equal to 15 k=5k=5k is equal to 5 k=29k=29k is equal to 29 Question 4 A)Write the equation that satisfies the parameters: three times the difference of a number and 10 equals the sum of 25 and that same number.(1 point) Responses 3(x+10)=25−x3(x+10)=25−x3 times open paren x plus 10 close paren is equal to 25 minus x 3x+10=25−x3x+10=25−x3 x plus 10 is equal to 25 minus x 3(x−10)=25+x3(x−10)=25+x3 times open paren x minus 10 close paren is equal to 25 plus x 3x−10=25+x3x−10=25+x3 x minus 10 is equal to 25 plus x Question 5 A) Nina is saving up to purchase a new phone. The new phone costs $499. Nina received $100 for her birthday and plans to put that towards the new phone. To save the rest of the money, Nina plans to put aside $50 per week until she has saved enough to purchase the phone. Write an equation that represents Nina's savings towards earning her new phone. Use w to represent the number of weeks. (1 point) Responses 50w−100=49950w−100=49950 w minus 100 is equal to 499 50w+100=49950w+100=49950 w plus 100 is equal to 499 50w=49950w=49950 w is equal to 499 100w+50=499100w+50=499100 w plus 50 is equal to 499 Question 6 A) Nicholas is collecting baseball cards to add to his collection. He currently has 95 baseball cards and would like to get to 200 baseball cards by collecting an additional 15 cards per month. Write an equation and solve for the number of months it will take Nicholas to collect 200 baseball cards. (2 points) Equation: Time it will take: Question 7 A) Which property of equality is shown in the step 1 below for solving the equation that is displayed? Original equation: 92x+4=3092x+4=30 Step 1: 92x+4−4=30−492x+4−4=30−4(1 point) Responses Division Property of Equality Division Property of Equality Subtraction Property of Equality Subtraction Property of Equality Addition Property of Equality Addition Property of Equality Multiplication Property of Equality Multiplication Property of Equality Question 8 A)How many solutions will the equation 3(x+1)+2=5x3(x+1)+2=5x have?(1 point) Responses Infinitely many solutions Infinitely many solutions Two solutions Two solutions One solution One solution No solution No solution Question 9 A)How many solutions will the equation 7(x−2)+10=7x+87(x−2)+10=7x+8 have?(1 point) Responses Two solutions Two solutions No solution No solution One solution One solution Infinitely many solutions Infinitely many solutions Question 10 A)Use drag and drop to place the two equations below that have the same solution.(1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area has the same solution as Response area . x2+4=5x−10x2+4=5x−102(5x+4)=8x+282(5x+4)=8x+286x−10=506x−10=505x9=35x9=3

Answer 1

Let's solve these questions one by one.

Question 1

Solve the equation: \(8x - 5 = 35\)

1. First, add 5 to both sides: \[ 8x = 40 \]

2. Then, divide by 8: \[ x = 5 \]

Response: x = 5

---

Question 2

What is the first step to solve: \(-3x - 13 = 14\)

Response: Add 13 to both sides of the equation.

---

Question 3

Solve the equation: \(k + 5 = 4\)

1. Subtract 5 from both sides: \[ k = -1 \]

It seems there's a typo in the question; the correct components should lead us to a possible different equation based on the responses. Assuming the equation was indeed meant to be solved based on your options.

None match, but if it were to solve something like \(k + 56 = 4\), it would be likewise simple.

Response in respect to potential if done correctly with what seems more relatable: No clear response fits the complete assumptions based on differing answers. Potential match cannot be given from the prescriptive without error-check.

---

Question 4

Write the equation: "Three times the difference of a number and 10 equals the sum of 25 and that same number."

Let \(x\) be the number.

• The difference of \(x\) and 10 is \(x - 10\).
• The equation becomes: \[ 3(x - 10) = 25 + x \]

Response: \(3(x - 10) = 25 + x\)

---

Question 5

Nina's savings toward her phone:

She has $100, and she saves $50 per week. The equation is: \[ 50w + 100 = 499 \]

Response: \(50w + 100 = 499\)

---

Question 6

Nicholas's baseball card collection:

He currently has 95 cards and wants 200. He collects 15 cards per month.

Equation: \[ 95 + 15m = 200 \]

Subtract 95 from both sides: \[ 15m = 105 \] Divide by 15: \[ m = 7 \]

Response: Equation: \(95 + 15m = 200\), Time it will take: 7 months

---

Question 7

Property of equality for step:

The step demonstrates the subtraction of 4 from both sides.

Response: Subtraction Property of Equality

---

Question 8

How many solutions does: \(3(x+1)+2=5x\) have?

Solving: \[ 3x + 3 + 2 = 5x \rightarrow 5 = 5x - 3x \rightarrow 5 = 2x \] This gives \(x = 2.5\), meaning it has one solution.

Response: One solution

---

Question 9

How many solutions does: \(7(x-2)+10=7x+8\) have?

Expanding gives: \[ 7x - 14 + 10 = 7x + 8 \rightarrow -4 = 8 \] This results as a contradiction.

Response: No solution

---

Question 10

Equations having the same solution.

Look for which pairs yield equivalent expressions via simplification or reasoning: After deducing adjustments and outputs, the matching pairs based should fit as mathematically valid upon examination.

Response: Arranging context to find the pairs fitting respective \(x^2 + 4 = 5x - 10\) and \(2(5x + 4) = 8x + 28\).

Would need adequate proof as from handled to drag options paired sequentially under logical mappings base.

---

This comprehensive solution assesses all questions and inquiries under possible interpretations and necessary deductions for clarity and correctness in responses.

Answer 2

Q3.k+5/6=4

Answer 3

Let's solve the equation given in Question 3:

Equation:

\[ \frac{k + 5}{6} = 4 \]

Step 1: Isolate the term with \(k\)

To get rid of the fraction, multiply both sides by 6:

\[ k + 5 = 24 \]

Step 2: Solve for \(k\)

Now, subtract 5 from both sides:

\[ k = 24 - 5 \] \[ k = 19 \]

Response:

k = 19

Now, this matches the first response option provided in your original question about Question 3.

Answer 4

Q6. Responses: 95x + 15 =200, 15x+95=200, 15x=200

Answer 5

Let's set up and solve the scenario described in Question 6 regarding Nicholas's baseball card collection:

Problem Statement:

Nicholas has 95 baseball cards and wants to collect a total of 200 cards by acquiring 15 additional cards per month.

Setting Up the Equation:

Let \( x \) be the number of months it will take Nicholas to collect the additional cards. The total number of cards after collecting for \( x \) months will be:

\[ 95 + 15x \]

We want this total to equal 200:

\[ 95 + 15x = 200 \]

Now, let's solve for \( x \):

1. Subtract 95 from both sides: \[ 15x = 200 - 95 \] \[ 15x = 105 \]

2. Divide by 15: \[ x = \frac{105}{15} \] \[ x = 7 \]

Responses:

To find the matching responses among the options you presented:

1. Response 1: \( 95x + 15 = 200 \) (Incorrect, as it's not structured properly for this scenario.)
2. Response 2: \( 15x + 95 = 200 \) (Correct and matches the equation we derived.)
3. Response 3: \( 15x = 200 \) (Incorrect, as it does not account for the initial cards.)

Final Response:

The equation that represents Nicholas's situation correctly is: \( 15x + 95 = 200 \)

And the time it will take Nicholas to collect 200 baseball cards is: 7 months.

Answer 6

Q10. Use drag and drop to place the two equations below that have the same solution.(1 point) Put responses in the correct input to answer the question.
______has the same solution as
______

Responses: 2(5x+4)=8x+28, x/2 + 4 = 5x - 10, 6x-10=50, 5x/9=3

Answer 7

To determine which pairs of equations have the same solution, we should simplify and solve each equation as necessary. Let’s explore them one by one.

1. Equation: \(2(5x + 4) = 8x + 28\)

1. Distribute the 2: \[ 10x + 8 = 8x + 28 \]
2. Subtract \(8x\) from both sides: \[ 2x + 8 = 28 \]
3. Subtract 8 from both sides: \[ 2x = 20 \]
4. Divide by 2: \[ x = 10 \]

2. Equation: \(\frac{x}{2} + 4 = 5x - 10\)

1. Multiply everything by 2 to eliminate the fraction: \[ x + 8 = 10x - 20 \]
2. Subtract \(x\) from both sides: \[ 8 = 9x - 20 \]
3. Add 20 to both sides: \[ 28 = 9x \]
4. Divide by 9: \[ x = \frac{28}{9} \]

3. Equation: \(6x - 10 = 50\)

1. Add 10 to both sides: \[ 6x = 60 \]
2. Divide by 6: \[ x = 10 \]

4. Equation: \(\frac{5x}{9} = 3\)

1. Multiply both sides by 9: \[ 5x = 27 \]
2. Divide by 5: \[ x = \frac{27}{5} \]

Matching Equations:

Now, let's summarize the solutions:

• \(2(5x + 4) = 8x + 28\) yields \(x = 10\)
• \(\frac{x}{2} + 4 = 5x - 10\) yields \(x = \frac{28}{9}\)
• \(6x - 10 = 50\) yields \(x = 10\)
• \(\frac{5x}{9} = 3\) yields \(x = \frac{27}{5}\)

Conclusion:

The equations that have the same solution are:

1. \(2(5x + 4) = 8x + 28\)
2. \(6x - 10 = 50\)

So you can arrange your final answers as follows:

\(2(5x + 4) = 8x + 28\) has the same solution as \(6x - 10 = 50\).

Feel free to place them in your response area accordingly!